Workshop on Numerical Methods for Multi-material Fluid Flows, Prague, Czech Republic, September 10-14, 2007 Sandia is a multiprogram laboratory operated.

Slides:



Advertisements
Similar presentations
ASME-PVP Conference - July
Advertisements

Experiment #5 Momentum Deficit Behind a Cylinder
Navier-Stokes.
Continuity Equation. Continuity Equation Continuity Equation Net outflow in x direction.
Effects of Bulk Viscosity on p T -Spectra and Elliptic Flow Parameter Akihiko Monnai Department of Physics, The University of Tokyo, Japan Collaborator:
Dr. Kirti Chandra Sahu Department of Chemical Engineering IIT Hyderabad.
A J Barlow, September 2007 Compatible Finite Element multi-material ALE Hydrodynamics Numerical methods for multi-material fluid flows 10-14th September.
Section 4: Implementation of Finite Element Analysis – Other Elements
Introduction to numerical simulation of fluid flows
1 MECH 221 FLUID MECHANICS (Fall 06/07) Tutorial 7.
1 Internal Seminar, November 14 th Effects of non conformal mesh on LES S. Rolfo The University of Manchester, M60 1QD, UK School of Mechanical,
12/21/2001Numerical methods in continuum mechanics1 Continuum Mechanics On the scale of the object to be studied the density and other fluid properties.
University of North Carolina - Chapel Hill Fluid & Rigid Body Interaction Comp Physical Modeling Craig Bennetts April 25, 2006 Comp Physical.
16/12/ Texture alignment in simple shear Hans Mühlhaus,Frederic Dufour and Louis Moresi.
James Sprittles ECS 2007 Viscous Flow Over a Chemically Patterned Surface J.E. Sprittles Y.D. Shikhmurzaev.
Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA Slide 1 The Implementation of a General Higher-Order Remap Algorithm.
Fluids. Eulerian View  In a Lagrangian view each body is described at each point in space. Difficult for a fluid with many particles.  In an Eulerian.
Conservation Laws for Continua
Review (2 nd order tensors): Tensor – Linear mapping of a vector onto another vector Tensor components in a Cartesian basis (3x3 matrix): Basis change.
Department of Aerospace and Mechanical Engineering A one-field discontinuous Galerkin formulation of non-linear Kirchhoff-Love shells Ludovic Noels Computational.
Relativistic Smoothed Particle Hydrodynamics
SAND C Limited Artificial Viscosity and Hyperviscosity Based on a Nonlinear Hybridization Method September 7, 2011 Bill Rider, Ed Love, and G.
The Instability of Laminar Axisymmetric Flows. The search of hydrodynamical instabilities of stationary flows is classical way to predict theoretically.
Smoothed Particle Hydrodynamics
CEE 262A H YDRODYNAMICS Lecture 5 Conservation Laws Part I 1.
Chapter 9: Differential Analysis of Fluid Flow SCHOOL OF BIOPROCESS ENGINEERING, UNIVERSITI MALAYSIA PERLIS.
Page 1 JASS 2004 Tobias Weinzierl Sophisticated construction ideas of ansatz- spaces How to construct Ritz-Galerkin ansatz-spaces for the Navier-Stokes.
AOE 5104 Class 7 Online presentations for next class: Homework 3
Algorithm Developments in Alegra Guided by Testing W. Rider, A. Robinson, G. Weirs, C. Ober, E. Love, H. Hanshaw, R. Lemke, G. Scovazzi, J. Shadid, J.
AMS 691 Special Topics in Applied Mathematics Lecture 3 James Glimm Department of Applied Mathematics and Statistics, Stony Brook University Brookhaven.
Brookhaven Science Associates U.S. Department of Energy MUTAC Review January 14-15, 2003, FNAL Target Simulations Roman Samulyak Center for Data Intensive.
A conservative FE-discretisation of the Navier-Stokes equation JASS 2005, St. Petersburg Thomas Satzger.
1 MAE 5130: VISCOUS FLOWS Conservation of Mass September 2, 2010 Mechanical and Aerospace Engineering Department Florida Institute of Technology D. R.
Mass Transfer Coefficient
J.-Ph. Braeunig CEA DAM Ile-de-FrancePage 1 Jean-Philippe Braeunig CEA DAM Île-de-France, Bruyères-le-Châtel, LRC CEA-ENS Cachan
Measurements in Fluid Mechanics 058:180:001 (ME:5180:0001) Time & Location: 2:30P - 3:20P MWF 218 MLH Office Hours: 4:00P – 5:00P MWF 223B-5 HL Instructor:
Panel methods to Innovate a Turbine Blade-1 P M V Subbarao Professor Mechanical Engineering Department A Linear Mathematics for Invention of Blade Shape…..
1996 Eurographics Workshop Mathieu Desbrun, Marie-Paule Gascuel
© Fluent Inc. 11/24/2015J1 Fluids Review TRN Overview of CFD Solution Methodologies.
Ale with Mixed Elements 10 – 14 September 2007 Ale with Mixed Elements Ale with Mixed Elements C. Aymard, J. Flament, J.P. Perlat.
HEAT TRANSFER FINITE ELEMENT FORMULATION
A Dirichlet-to-Neumann (DtN)Multigrid Algorithm for Locally Conservative Methods Sandia National Laboratories is a multi program laboratory managed and.
Louisiana Tech University Ruston, LA Boundary Layer Theory Steven A. Jones BIEN 501 Friday, April
CIS/ME 794Y A Case Study in Computational Science & Engineering 2-D conservation of momentum (contd.) Or, in cartesian tensor notation, Where repeated.
Discretization Methods Chapter 2. Training Manual May 15, 2001 Inventory # Discretization Methods Topics Equations and The Goal Brief overview.
A New Discontinuous Galerkin Formulation for Kirchhoff-Love Shells
AMS 691 Special Topics in Applied Mathematics Lecture 3
Flow and Dissipation in Ultrarelativistic Heavy Ion Collisions September 16 th 2009, ECT* Italy Akihiko Monnai Department of Physics, The University of.
M. Khalili1, M. Larsson2, B. Müller1
Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation,
Model Anything. Quantity Conserved c  advect  diffuse S ConservationConstitutiveGoverning Mass, M  q -- M Momentum fluid, Mv -- F Momentum fluid.
Biomechanics Mechanics applied to biology –the interface of two large fields –includes varied subjects such as: sport mechanicsgait analysis rehabilitationplant.
Computational Fluid Dynamics Lecture II Numerical Methods and Criteria for CFD Dr. Ugur GUVEN Professor of Aerospace Engineering.
A hyperbolic model for viscous fluids First numerical examples
Finite Element Method in Geotechnical Engineering
Convection-Dominated Problems
A rotating hairy BH in AdS_3
FLUID DYNAMICS Made By: Prajapati Dharmesh Jyantibhai ( )
Introduction to Fluid Mechanics
Convergence in Computational Science
Effects of Bulk Viscosity at Freezeout
Konferanse i beregningsorientert mekanikk, Trondheim, Mai, 2005
University of Liège Department of Aerospace and Mechanical Engineering
Objective Numerical methods Finite volume.
Thermal Micro-actuators for Out-of-plane Motion
FLUID MECHANICS REVIEW
Effects of Bulk Viscosity on pT Spectra and Elliptic Flow Coefficients
MAE 3241: AERODYNAMICS AND FLIGHT MECHANICS
topic11_shocktube_problem
FLUID MECHANICS - Review
Presentation transcript:

Workshop on Numerical Methods for Multi-material Fluid Flows, Prague, Czech Republic, September 10-14, 2007 Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under contract DE-AC04-94AL A multi-scale Q1/P0 approach to Lagrangian Shock Hydrodynamics Guglielmo Scovazzi 1431 Computational Shock- and Multi-physics Department Sandia National Laboratories, Albuquerque (NM) Research collaborators: Edward Love, 1431 Sandia National Laboratories Mikhail Shashkov, Group T-7, Los Alamos National Laboratory

Scovazzi-Love-Shashkov, “VMS-hydrodynamics” Motivation and outline Q1/Q1, P1/P1-Lagrangian hydrodynamics with SUPG/VMS  Promising results for Q1/Q1 and P1/P1 finite elements  Scovazzi-Christon-Hughes-Shadid, CMAME 196 (2007) pp )  Scovazzi, CMAME 196 (2007) pp  Is it possible to extend some of the ideas to Q1/P0?  Is it possible to design multi-scale hourglass controls? A new approach for Q1/P0 finite elements in fluids  A pressure correction operator provides hourglass stabilization  A Clausius-Duhem equality is used to detect instabilities  The stabilization counters numerical entropy production  The approach is applicable to ALE (Lagrangian+remap) algorithms  Promising results in 2D and 3D compressible flow computations

Scovazzi-Love-Shashkov, “VMS-hydrodynamics” Lagrangian hydrodynamics equations Lagrangian framework and constitutive relations: Materials with a caloric EOS

Scovazzi-Love-Shashkov, “VMS-hydrodynamics” Momentum equation Energy equation Lagrangian hydrodynamics equations Mid-point time integrator: Zero traction BCs Total energy is conserved (even with mass lumping!) Mass equation = piecewise linear kinematic vars. piecewise constant thermodynamic vars. =

Scovazzi-Love-Shashkov, “VMS-hydrodynamics” Algorithm and discrete energy conservation Every iteration:  Mass  Momentum  Angular momentum  Total energy are conserved 3D Sedov test, energy history Scale is Total energy relative error To ensure conservation

Scovazzi-Love-Shashkov, “VMS-hydrodynamics” Lagrangian hydrodynamics equations Variational Multi-scale (VMS) Stabilization: Pressure correction VMS Assumptions: 1. 2.Quadratic fine-scale terms are neglected 3.Fine-scale displacements are neglected 4. is negligible 5.Time derivatives of fine scales are neglected 6.The divergence of fine-scale velocity is neglected 

Scovazzi-Love-Shashkov, “VMS-hydrodynamics” Lagrangian hydrodynamics equations VMS fine-scale problem through linerarization: whereand Physical interpretation: The pressure residual samples the production of entropy due to the numerical approximation (Clausius-Duhem) needs multi-point evaluation

Scovazzi-Love-Shashkov, “VMS-hydrodynamics” Lagrangian hydrodynamics equations Numerical interpretation of VMS mechanisms: Given the decomposition and recalling thataway from shocks Energy: Momentum:

Scovazzi-Love-Shashkov, “VMS-hydrodynamics” Acoustic pulse computations Initial mesh “seeded” with an hourglass pattern

Scovazzi-Love-Shashkov, “VMS-hydrodynamics” A closer look at the artificial viscosity Artificial viscosity à la von-Neumann/Richtmyer: Sketches of element length scales

Scovazzi-Love-Shashkov, “VMS-hydrodynamics” VMS-control No hourglass control Two-dimensional Sedov blast test Mesh deformation, pressure, and density (45x45 mesh) Mesh deformation Element density contoursNum. vs exact solution Pressure Density

Scovazzi-Love-Shashkov, “VMS-hydrodynamics” VMS stabilization in three dimensions Hourglass “dilemma” and its space decomposition: Additional deviatoric hourglass viscosity Modes with non-zero divergence Pointwise divergence-free modes (non-homogenous shear)

Scovazzi-Love-Shashkov, “VMS-hydrodynamics” Three-dimensional tests on Cartesian meshes 3D-Noh test on cartesian mesh (density) Noh test, 30 3 mesh, density Sedov test, 20 3 mesh, density Flanagan-Belytschko cannot solve both, VMS does:

Scovazzi-Love-Shashkov, “VMS-hydrodynamics” Summary and future directions A new paradigm for hourglass control  Strongly based on physics  A Clausius-Duhem term detects instabilities  In 3D, discriminates between physical and numerical effects Future work  Complete investigation in 3D computations  More complex equations of state  Generalizations to solids (no need for deviatoric hourglass viscosity)  Application to ALE (Lagrangian+remap)  Artificial viscosity Contact & pre-prints: Contact & pre-prints:

Scovazzi-Love-Shashkov, “VMS-hydrodynamics” Tensor artificial viscosity Two-dimensional Noh implosion test Mesh distortion comparison No spurious jets Pressure-like artificial viscosity Spurious jets Radial tri-sector mesh